Sequence Hunt

You are given two integers, \(N\) and \(K\). Your task is to generate a sequence of \(N\) distinct integers such that:

1. Each integer in the sequence is within the range \(1\) to \(K\) (inclusive).
2. There is no subsequence of size \(3\) where the difference between consecutive terms remains constant.

In other words, you need to find a sequence \(a_1, a_2, ..., a_N\) such that for any indices \(p < q < r\), the difference \(a_q - a_p\) is not equal to \(a_r - a_q\).

Input Format

Two space-separated integers: \(N\) representing the length of the sequence and \(K\) representing the range upper limit for the numbers in the sequence.

Output Format

A sequence of \(N\) space separated integers. In case of multiple valid answers, print any.

Constraints

• \[1 \leq N \leq 10^4\]
• \[1 \leq K \leq 2 \times 10^6\]

Subtasks

1. (15 points) \(1 \leq N \leq 10\) and $ K = 2 \times 10^6$
2. (15 points) \(1 \leq N \leq 10\) and $ K = N$
3. (15 points) \(1 \leq N \leq 250\) and $ K = 4 \times 10^3$
4. (15 points) \(1 \leq N \leq 10^4\) and $ K = 2 \times 10^6$
5. (40 points) \(1 \leq N \leq 10^4\) and $ K = N$

Limits

• Memory - 256MB
• Time - 2 seconds

Sample Input 0

4 7

Sample Output 0

1 2 4 5